# Error Coding for Engineers

A. Houghton
Springer, Jan 1, 2001 - Computers - 246 pages
Error Coding for Engineers provides a useful tool for practicing engineers, students, and researchers, focusing on the applied rather than the theoretical. It describes the processes involved in coding messages in such a way that, if errors occur during transmission or storage, they are detected and, if necessary, corrected. Very little knowledge beyond a basic understanding of binary manipulation and Boolean algebra is assumed, making the subject accessible to a broad readership including non-specialists. The approach is tutorial: numerous examples, illustrations, and tables are included, along with over 30 pages of hands-on exercises and solutions. Error coding is essential in many modern engineering applications. Engineers involved in communications design, DSP-based applications, IC design, protocol design, storage solutions, and memory product design are among those who will find the book to be a valuable reference. Error Coding for Engineers is also suitable as a text for basic and advanced university courses in communications and engineering.

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### Contents

 Introduction 1 12 The Hamming Bound 4 13 The Gilbert Bound 6 14 Where do Errors Come From? 7 15 A Brief History of Error Coding 12 16 Summary 13 A Little Maths 15 21 Polynomials and Finite Fields 16
 82 Punctured Codes 121 83 Interleaving 125 84 Error Forecasting 130 85 Discussion 131 Convolutional Coding 133 91 Error Correction with Convolutional Codes 135 92 Finding the Correct Path 136 93 Decoding with Soft Decisions 138

 22 Manipulating Field Elements 19 23 Summary 24 Error Detection 25 32 The Cyclic Redundancy Check 27 33 Longhand Calculation of the CRC 28 34 Performance 31 35 Hardware Implementation 32 36 TableBased Calculation of the CRC 35 37 Discussion 39 Error Correction by Parity 41 41 Correcting a Single Bit 43 42 Extending the Message Size 45 Error Correction Using the CRC 49 51 A Hardware Error Locator 52 52 Multiple Bit Errors 53 53 Expurgated Codes 54 54 The Perfect Golay Code 56 55 Fire Codes 63 ReedMuller Codes 67 62 Encoding With the Hadamard Matrix 74 63 Discussion 77 ReedSolomon Codes 79 72 Calculating Check Symbols for One Error 80 73 Correcting Two Symbols 83 74 Error Correction in the Frequency Domain 88 75 Recursive Extension 91 76 The BerlekampMassey Algorithm 97 77 The Forney Algorithm 100 78 MixedDomain Error Coding 101 79 Higher Dimensional Data Structures 107 710 Discussion 118 Augmenting Error Coding 119
 94 Performance of Convolutional Codes 140 95 Concatenated Codes 141 96 Iterative Decoding 142 97 Turbo Decoding 143 98 Discussion 144 Hardware 147 102 Multiplication 149 103 Division 153 104 Logs and Exponentials 158 105 Reciprocal 160 106 Discussion 164 Bit Error Rates 165 112 Estimating the Bit Error Rate 166 113 Applications 172 114 Discussion 176 Exercises 177 122 CRC Exercises 178 123 Finite Field Algebra 180 124 Convolutional Coding Exercises 183 126 Solutions to Parity Exercises 184 127 Solutions to CRC Exercises 186 128 Solutions to Finite Field Algebra 192 129 Solutions to Convolutional Coding 202 1210 Solutions to Other Codes 203 1211 Closing Remarks 208 Primitive Polynomials 211 The Golay Code 219 Solving for Two Errors 223 Solving some Key Equations 229 Software Library 233 Index 245 Copyright

### References from web pages

andy houghton libri - I Libri dell'autore: Andy Houghton ...
Error Coding for Engineers · Error Coding for Engineers di A. Houghton, Andy Houghton - Kluwer Academic Publishers - January 2002. Prezzo: € 223.85 ...
www.libreriauniversitaria.it/ books-author_andy+houghton-andy+houghton.htm